Question

This question might be elementary, but it is genuine. I realise that some users might downvote the question for being so basic, but I urge them to be a little merciful, and help out a confused high school student,

If a gas is expanded at a constant temperature then, according to Boyles' Law, P∝1V (if n an T are constant). According to Avogadro's Law, V∝n
(if P and T are constant). We know that T is constant, but what about P
and n? If n is constant, then Boyles' Law is valid. P∝1V ie. the pressure decreases on expanding the gas. If P is constant, then Avogadro's Law is valid. V∝n ie. the number of moles increases on increasing the volume. However, this is found to be false.

Furthermore, intuitively, we know that for an ideal gas, n=VgasVmolar, and here, Vgas continuously increases, indicating that n should also continuously increase. This doubt stemmed from a question from a question bank which prepares Indian students for a popular competitive engineering exam called JEE. The question, which has multiple correct options, reads:

If a gas expands at constant temperature :

(A) the pressure decreases

(B) the kinetic energy of the molecules remains the same

(C) the K.E. of the molecules decrease

(D) the number of molecules of the gas increase

I know that B is certainly correct, as the average kinetic energy of each molecule A.K.E.=32RT, and temperature is constant. My doubt was in options (A) and (D). For this question, (B) and (A) are the only correct answers and (D) is wrong, but I didn't understand the rationale of (A) being correct and (D) being wrong. If someone could explain why the number of moles of a gas doesn't increase despite the volume increasing i.e. it is expanded, as well as the reasoning of answering the JEE question bank question, it would be very helpful.

Edit: My doubt has been clarified by user Maurice. Here, the number of moles remains constant as no chemical reaction is taking place for them to increase. So Boyle's Law is valid, and the pressure decreases due to the increase in volume.

Answer 1

Boyle's Law states that if a gas is expanded at a constant temperature, the pressure decreases. The number of moles of a gas remains constant when the gas is expanded at a constant temperature as stated by Avogadro's Law.

Step-by-step explanation:

According to Boyle's Law, if a gas is expanded at a constant temperature, the pressure decreases. This means that option (A) the pressure decreases is correct. The reasoning behind this is that as the volume increases, the gas molecules have more space to move around, resulting in fewer collisions with the walls of the container, leading to a decrease in pressure.

Option (D) the number of molecules of the gas increases is incorrect because the number of moles of a gas remains constant when the gas is expanded at a constant temperature and there are no chemical reactions taking place. This is due to Avogadro's Law which states that at constant pressure and temperature, the volume of a gas is directly proportional to the number of moles of gas present. So, when the volume increases, the number of moles of gas remains the same.